Modal logic as metalogic

Abstract
The goal of this paper is to show how modal logic may be conceived as recording the derived rules of a logical system in the system itself. This conception of modal logic was propounded by Dana Scott in the early seventies. Here, similar ideas are pursued in a context less classical than Scott's.First a family of propositional logical systems is considered, which is obtained by gradually adding structural rules to a variant of the nonassociative Lambek calculus. In this family one finds systems that correspond to the associative Lambek calculus, linear logic, relevant logics, BCK logic and intuitionistic logic. Above these basic systems, sequent systems parallel to the basic systems are constructed, which formalize various notions of derived rules for the basic systems. The deduction theorem is provable for the basic systems if, and only if, they are at least as strong as systems corresponding to linear logic, or BCK logic, depending on the language, and their deductive metalogic is not stronger than they are.
Keywords modal logic  substructural logics  derived rules  deduction theorem  functional completeness in categories
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,360
External links
  •   Try with proxy.
  • Through your library Configure
    References found in this work BETA
    Kosta Došen (1992). Modal Translations in Substructural Logics. Journal of Philosophical Logic 21 (3):283 - 336.
    Kosta Došen (1985). Sequent-Systems for Modal Logic. Journal of Symbolic Logic 50 (1):149-168.
    Citations of this work BETA
    Kosta Došen (1992). Modal Translations in Substructural Logics. Journal of Philosophical Logic 21 (3):283 - 336.
    Similar books and articles
    Analytics

    Monthly downloads

    Added to index

    2009-01-28

    Total downloads

    19 ( #74,849 of 1,089,047 )

    Recent downloads (6 months)

    1 ( #69,722 of 1,089,047 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature


    Discussion
    Start a new thread
    Order:
    There  are no threads in this forum
    Nothing in this forum yet.